For S1,|z−1|≤√2,....(i) z lies on and inside the circle of radius √2 units and centre (1,0). For S2, let z=x+iy Now, (1−i)(z)=(1−i)(x+iy) =x+iy−ix+y =(x+y)+i(y−x) ∴Re[(1−i)z]=(x+y), which is greater than or equal to one. i.e., x+y≥1...(ii) Also, for S3, Let z=x+iy ∴Im(z)=y, which is less than or equal to one. i.e., y≤1 ....(iii) Concept Draw the graph of Eqs. (i), (ii) and (iii) and then select the common region bounded by Eqs. (i), (ii) and (iii) for S1∩S2∩S3.
